My Notes O Ask Your Teac 9. 1.7V10 points I Previous Answers DevcreStat? 5.P030.

Question

My Notes O Ask Your Teac 9. 1.7V10 points I Previous Answers DevcreStat? 5.P030.alt. It is known that 75% of all brand A zip drives work in satisfactory manner throughout the warranty period (are "successes"). Suppose that n-10 drives are randomly selected. Let X-the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic. Hint: One possible value Xir is .3, corresponding to X 3. What is the probability of this value (what kind of random veriable is X)7] (Give enswers accurate to J decimal places.) X 0.6 p(x/n) Find the mean and variance tor Xin trom its sampling distribution. mean varlance

Explanation / Answer

Solution:- given that n = 10 , p = 0.75

0.056

mean =   = xp(x) = 7.5001 = 7.5(rounded)

variance = ^2 = x^2p(x) ^2 = 1.8739 = 1.874 (rounded)

x 0 1 2 3 4 5 6 7 8 9 10 x/n 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p(x/n) 0 0 0 0.003 0.016 0.058 0.146 0.250 0.282 0.188

0.056

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